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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2012, Issue 4(29), Pages 146–153
DOI: https://doi.org/10.14498/vsgtu1095
(Mi vsgtu1095)
 

Mathematical Modeling

Percolation of the prolate ellipsoids of rotation in the continuum

M. M. Buzmakova

Astrakhan State University, Astrakhan, Russia (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: Continuum percolation of the hard prolate ellipsoids of rotation with permeable shell has been investigated. It is the model of phase transition sol–gel. Ellipsoids are located in the cube randomly. For each set of parameters 100 tests are spent. For each test the finding of the percolation cluster is the main task. The fraction of the packing for which the probability of the percolation cluster appearance is equal 0.5, is called a percolation threshold. Value of the percolation threshold corresponds to the gel point. Dependence of value of the percolation threshold on thickness of permeable shell and aspect ratio has been obtained. In addition to the percolation threshold the other characteristics of the model have been obtained, such as: the size distribution of clusters, the average cluster size, the strength and the fractal dimension of the percolation cluster, the average value and the distribution of neighbors of an element, the critical exponents.
Keywords: percolation, gelation, phase transitions.
Original article submitted 09/VI/2012
revision submitted – 25/IX/2012
Bibliographic databases:
Document Type: Article
UDC: 519.68:[5/6+3]+004.94+544.015.4+544.022.822
MSC: Primary 60K35; Secondary 82B43, 82B26, 82B21
Language: Russian
Citation: M. M. Buzmakova, “Percolation of the prolate ellipsoids of rotation in the continuum”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(29) (2012), 146–153
Citation in format AMSBIB
\Bibitem{Buz12}
\by M.~M.~Buzmakova
\paper Percolation of the prolate ellipsoids of rotation in the continuum
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 4(29)
\pages 146--153
\mathnet{http://mi.mathnet.ru/vsgtu1095}
\crossref{https://doi.org/10.14498/vsgtu1095}
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  • https://www.mathnet.ru/eng/vsgtu/v129/p146
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